Believable

to have confidence in the truth, the existence, or the reliability of something, although without absolute proof that one is right in doing so:
Only if one believes in something can one act purposefully.
to have confidence or faith in the truth of (a positive assertion, story, etc.); give credence to.
to have confidence in the assertions of (a person).
to have a conviction that (a person or thing) is, has been, or will be engaged in a given action or involved in a given situation:
The fugitive is believed to be headed for the Mexican border.
to suppose or assume; understand (usually followed by a noun clause):
I believe that he has left town.
believe in,

to be persuaded of the truth or existence of:
to believe in Zoroastrianism; to believe in ghosts.
to have faith in the reliability, honesty, benevolence, etc., of:
I can help only if you believe in me.

make believe. make1 (def 68).
Contemporary Examples

‘Monsieur Lazhar’ Tackles Immigration in Imaginative Canadian Film Stephen Farber April 12, 2012
Don’t Let Settlements Define Israel Justin Green January 14, 2013
Sex Won’t Kill Young Adult Heroines: ‘Divergent’ and Rape Culture Amy Zimmerman March 27, 2014
Why You’re Happily Married and Having an Affair Ryan Selzer November 1, 2014
‘Catching Fire’: How Jennifer Lawrence Learned to Shoot a Bow and Arrow Kevin Fallon November 25, 2013

Historical Examples

K Mary Roberts Rinehart
The White Blackbird Hudson Douglas
T. Tembarom Frances Hodgson Burnett
Bear Trap Alan Edward Nourse
The Game Jack London

verb
(transitive; may take a clause as object) to accept (a statement, supposition, or opinion) as true: I believe God exists
(transitive) to accept the statement or opinion of (a person) as true
(intransitive) foll by in. to be convinced of the truth or existence (of): to believe in fairies
(intransitive) to have religious faith
(when transitive, takes a clause as object) to think, assume, or suppose: I believe that he has left already
(transitive; foll by of; used with can, could, would, etc) to think that someone is able to do (a particular action): I wouldn’t have believed it of him
adj.
v.

believe it or not
believe one’s ears